Download PHY492: Nuclear & Particle Physics Lecture 24 Exam 2 Particle Detectors

PHY492: Nuclear & Particle Physics
Lecture 24
Exam 2
Particle Detectors
Exam 2
April 16, 2007
Carl Bromberg - Prof. of Physics
2
Exam 2
2. Short Answer [4 pts each]
a) To describe the QCD color quantum numbers of quarks and gluons, how many
colors are involved and give them relevant names.
There are 3 colors and 3 anti-colors, and gluons need both of them
Colors: red, blue, green ; Anti-colors: red, blue, green or cyan, yellow, magneta
b) Consider Electric Charge, Quark Flavor, Baryon #, Isospin, and Lepton #. List
those conserved by each of the three interactions other than gravity.
Interaction
Conserved
Strong
electric charge, quark flavor, baryon#, Isospin, lepton#
Weak
electric charge, baryon#, lepton#
Electromagnetic electric charge, quark flavor, baryon#, lepton#
c) Using the quantum numbers of the strange quark describe why the reaction
−
−
+
K p → Ξ + K can or cannot occur?
−
Since K = (s,u );
−
+
p = (uud); Ξ = (ssd); K = (s ,u) , reaction is allowed
Annihilation of a uu pair, and creation of an ss , generates the given final state.
April 16, 2007
Carl Bromberg - Prof. of Physics
3
Exam 2
d) What are the symbols and names of all three quarks with charge +2/3 .
(u) up; (c) charm; (t) top
0
0
e) In the oscillations of the B and B mesons what quantum characteristic is
violated, and what interaction must be involved.
0
0
The Bottom quark flavor is not conserved: B = (bd ), while B = (bd)
f) What matrix describes the mixing of neutrino flavor states as linear combinations
of the 3 neutrino mass states, ν1 , ν 2 ,ν 3 ? In what group (e.g., diagonal matrices ) is
the matrix? For what quarks does a similar matrix exist?
⎛ ν e ⎞ ⎡ U e1 U e2 U e3 ⎤ ⎛ ν1 ⎞
i) Neutrino mixing matrix U, such that ⎜ ν µ ⎟ = ⎢U µ1 U µ 2 U µ 3 ⎥ ⎜ ν 2 ⎟
⎥⎜ ⎟
⎜⎝ ν ⎟⎠ ⎢U
⎣ τ 1 Uτ 2 Uτ 3 ⎦ ⎝ ν3 ⎠
τ
ii) The mixing matrix is Unitary. iii) The –1/3 quarks, d,s,b mix into d’,s’,b’
g) Which Weak Bosons can be created in a collision of quarks?
All weak bosons can be created in a collision of quarks (Unless this is mentioned)
None, if you were thinking it had to be quark-antiquark or gluon-gluon collision.
April 16, 2007
Carl Bromberg - Prof. of Physics
4
Exam 2
h) The Cabibbo angle gives the mixing of which two quark mass states? d and s
(ds′′) = ⎡⎢⎣−cossinθθ
c
c
()
sin θ c ⎤ d
cosθ c ⎥⎦ s
i) What are the symbols and names of all three quarks with charge –1/3 .
(d) down; (s) strange; (b) bottom
−
+
j) The W boson can be produced in what QCD colors? Same question for W ?
±
The weak bosons, W , Z , are colorless particles. Their decay into a quark (color)
and an anti-quark (anti-color) must proceed where the anti-color corresponds to the
color.
April 16, 2007
Carl Bromberg - Prof. of Physics
5
Exam 2
B+ S +C
, where B is the
2
baryon number, S is the strangeness quantum number, and C is the charm quantum
number, is true for all meson and baryon states.
Show that this relationship also works for the quarks with B = 1 3 , the up and down
quarks in an Isospin = 1/2 doublet, and the strange and charm quarks as Isospin = 0
singlets.
5. [40 pts]The Gell-Mann Nishijima relation is, Q = I3 +
Quark
u
d
c
s
April 16, 2007
I3
+1/2
–1/2
0
0
B
1/3
1/3
1/3
1/3
S
0
0
0
–1
C
0
0
+1
0
I3+(B+S+C)/2
3/6+1/6 = +2/3
–3/6+1/6 = –1/3
0 + 2/3 = +2/3
0 –1/3 = –1/3
Q
+2/3
–1/3
+2/3
–1/3
Check
OK
OK
OK
OK
Carl Bromberg - Prof. of Physics
6
Charged particle induced ionization
• Moving particle, mass M, ionizes atoms in medium
dT
S(T ) = −
= nion I
dx
T : kinetic energy of moving particle
nion : number of electron-ion pairs unit path length
I : average energy electron-ion pair
• nion is particle velocity and charge dependent (Bethe and Bloch)
Stopping power
2 2 2
⎤
4π Q 2 e2 nZ ⎡ ⎛ 2me c γ β ⎞
2
S(T ) =
−β ⎥
⎢ ln ⎜
⎟
2 2
I
me β c ⎢⎣ ⎝
⎠
⎥⎦
S(T ) ∝
1
1
=
β 2c2 v 2
β = v/c = < 0.8
heavy ionization
April 16, 2007
γ =
E
pc
p
;
β
=
;
γβ
=
E
Mc
Mc 2
S minimizes, γβ  3
S ∝ ln γ
when β ~ 0.95
ultra relativistic
minimum ionization
rise of ionization
Carl Bromberg - Prof. of Physics
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Ionization in gases (relevant to all particles)
Ionization vs momentum
Normalized Ionization vs γβ
for various particle masses
Argon Gas
γβ =
April 16, 2007
pc
Mc 2
Carl Bromberg - Prof. of Physics
8
Saturation of ionization in solids
• Relativistic rise of ionization is due to electric field
concentration perpendicular to direction of motion
• Atoms along the line of motion
see a stronger field as v -> c.
• Effect is largest in large Z
gases, e.g., Xe
• Solids polarize and shield
far electrons from field
April 16, 2007
effect saturates at only a
few % above the minimum
Carl Bromberg - Prof. of Physics
9
Minimum ionization in thin solids
Z : atomic number of medium
n : number of atoms/unit volume
ρ A0
n=
; A : atomic number of medium
A
dT
Z
S(T ) = −
∝ nZ = ρ A0
dx
A
• Units for energy loss
– Z/A ~ 0.4 at large A, energy loss proportional to density S~ρ,
– Divided by the density -> value nearly independent of material.
• (dE/dx) min tabularized for various materials in MeV/(g/cm2)
– Polystyrene scintillator: 1.95
ρscintillator = 1.03 g/cm 3
−
– Iron (steel) : 1.45
dT
dx
min
⎛ MeV ⎞
= 1.95 ⎜
ρ
= 2.0 MeV/cm
2 ⎟ Scintillator
⎝ g/cm ⎠
ρiron = 7.87 g/cm 3
dT
−
dx
min
⎛ MeV ⎞
= 1.45 ⎜
ρ = 11.4 MeV/cm
⎝ g/cm 2 ⎟⎠ iron
Relativistic muon loses ~2 MeV/cm in plastic, ~11.4 MeV/cm in Iron
April 16, 2007
Carl Bromberg - Prof. of Physics
10
High energy particles in matter
• Particles can be deflected, degraded or absorbed
• Characteristic length is particle, energy, and material dependent
Long lived particles (τ > 10-10 s)
• Muons (mass mµ ~ 200 me)
– lose energy mostly by ionization -> energy determines range
– rare energy loss by photon radiation in the EM field of nucleus
– very rare EM interaction on nuclear charges, nuclear disintegration
– deflection by multiple scatterings on atomic electrons
• Electrons and photons at high energy (T > 1 GeV)
– Electron radiates a photon: X0 is the “radiation length”
– Photon converts to e+e- pair: 9X0/7 is the “pair length”
– both only rarely collide with a nucleus
• Hadrons (proton, neutron, charged pi-meson, K-meson, ...)
– nuclear interactions; absorption length, Xabs proportional to density ρ
– additional hadrons often created
April 16, 2007
Carl Bromberg - Prof. of Physics
11
Muon multiple scattering
• 5 GeV muon (m=105.6 MeV/c2) through 1 m of steel looses about
1.1 GeV by ionization. Some atomic electrons are kicked hard.
• Muon will be deflected (either direction) with a probability
distribution that peaks at θ = 0 but spread by θrms.
θ rms ≈
20 MeV
β pc
L
X0
Iron X 0 = 1.76cm
θ rms
April 16, 2007
20 100
=
= 30 mr = 2o
5000 1.76
Carl Bromberg - Prof. of Physics
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Bremsstrahlung
• High energy electrons loose energy primarily by radiating photons
• The characteristic length, X0 is material dependent
• Kinetic energy (on average) will drop exponentially.
dT
dx
=−
Brem
T
X0
T = T0 e
−T X 0
• Photon energies are discrete with a
1/Eγ distribution
• Many low energy photons (even IR)
and a few high energy photons
April 16, 2007
Carl Bromberg - Prof. of Physics
13
Photons in matter
• E < 1 MeV, photoelectric absorption and Compton scattering
dominate the interactions of photons
• E = 1 - 10 MeV, Compton scattering dominates but pair production is
rising
• E > 10 MeV, pair production dominates the interactions
Cascading interactions
1.
2.
1 GeV photon enters a block of lead (X0 = 0.56 cm)
After 5 mm the photon produces a e+e- pair (0.4 and 0.6 GeV)
3.
After 3 mm the e+ “brems” a 100 MeV photon. After 6 mm the e“brems” a 300 MeV photon (e+ and e- are both 300 MeV).
4.
After a few more mm each, the 100 MeV and 300 MeV photons
pair produce, the 300 MeV e+ and e- both brems
5.
Repeats until photons and electrons drop below 1 MeV.
April 16, 2007
Carl Bromberg - Prof. of Physics
14
Measuring a particle’s momentum, energy, and mass
• Charged particle tracking
MWPC = Multi-Wire Proportional Chamber
– Gas: MWPC, Drift Chamber, GEM
GEM = Gas Electron Multiplier
– Solid state: Silicon, diamond
• Scintillators
– scintillation and conversion -> electronic signals
– Organic: Plastic, liquid hydrocarbon, fibers
– Inorganic: Crystals, liquid noble gas
• Calorimeters
– total absorption
– sampling
• Particle identification (ID)
– time of flight
– ionization
– Cerenkov light
– transition radiation
April 16, 2007
Carl Bromberg - Prof. of Physics
15
Momentum measurements
•Charge Q bending in a magnetic field
Relativistic
Derivation
p = γ mv
vdt
dp = pdθ = p
R
dp
v
= p = QvB
dt
R
p = QBR
•Transform to more useful units
p ≈ 0.3qBR
p in GeV/c, q in # of e's
B in Tesla, R in meters
April 16, 2007
Units transformation
(
−19
1 eV = 1.6 × 10−19 J q = Q 1.6 × 10 C
)
⎛ kg ⋅ m ⋅ s-1 ⎞ ⎡⎛ c ⎞ ⎛ e ⎞ ⎤
p = QBR ⎜ 1
⎥
⎟⎢
⎝ C ⋅ T ⋅ m ⎠ ⎣⎜⎝ c ⎟⎠ ⎜⎝ e ⎟⎠ ⎦
⎛ 3 × 108 eV/c ⎞
= qBR ⎜
⎟
T⋅m
⎝
⎠
⎛ GeV/c ⎞
= 0.3qBR ⎜
⎝ T ⋅ m ⎟⎠
Carl Bromberg - Prof. of Physics
16
Using the sagitta to find R
• Bending of elementary charge in a magnetic field
– large radius -> weak bending -> large momentum
– typically see only a small portion of the circle
– measurement of momentum is equivalent to a
measurement of the sagitta.
easy to show
R≈
2
L
, s << R
8s
s = sagitta
p = 0.3qBR
δp ⎛
8 ⎞
=⎜
δs
2
2⎟
⎝ 0.3qBL ⎠
p
δs is fixed by detectors
make δs as small as possible
• Momentum errors minimized by big B, or even better by big L
April 16, 2007
Carl Bromberg - Prof. of Physics
17
Basics of wire chamber tracking
–HV cathode
• Wire chamber features
– Isolated gas volume (“chamber”)
– Anode wire, Au plated W, dia. <50µ
Anode wire
GND potential
– Cathodes at high voltage
• Gas properties (big subject)
– Noble gas (Ar) no negative ions
–HV cathode
avalanche ~ 100µ from wire
– UV quencher (hydrocarbon)
– Cost
• Cheap (flow & exhaust)
• Expensive (recirculate & clean)
• Electronics
1 e -> 105 e
one electronics “channel”
– 1 circuit for each wire
– fast, low noise
– multi-channel ICs
April 16, 2007
Carl Bromberg - Prof. of Physics
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